Prompt: On page 64, Steve sets the stage for the "glimpses" he shares in Chapter 5. He offers us examples that he describes as engaging, concept-oriented, problem solving, problem driven mathematics.

What is your example? Have you seen it? Have you done it? Trying to do it? Got student work to show it?

I think chapter 5 is a fantastic read because all of the examples are great ways to bring the real world math into the classroom in a way that students are able to be part of something and make a real impact. A common challenge for many math teachers is to find ways to show students how math is applicable in "real life." Students always want to know when they would actually use the math we do. I have done these types of assignments with students in the past where I would set up a situation similar for students to solve. I love the idea of taking it to the next level and actually including local businesses.

Prompt: On page 64, Steve sets the stage for the "glimpses" he shares in Chapter 5. He offers us examples that he describes as engaging, concept-oriented, problem solving, problem driven mathematics.

What is your example? Have you seen it? Have you done it? Trying to do it? Got student work to show it?

My students are "embarking" (pun intended) on a project involving a trip on the Amtrak Downeaster from Brunswick to destination to be determined. They are using the Downeaster web site (http://www.amtrakdowneaster.com) to pick a town on the route between Brunswick and Boston where the train makes stops, research the attractions at the site, estimate the cost for 13 students and 2 adults for the round trip fare, cost of the attractions and any transportation needed to get from the train station to the attraction. They will also need to figure out travel time and time to visit the attraction they have chosen. In addition to the math we will be learning how to use google maps, google drive (presentation) and some other technology skills. The kids just started this project last week. They are enthusiastic right now. The class may end up on the train to Boston.

In response to this week's prompt.
What I've been seeing:
A sixth grade classroom learning about area and perimeter of two-dimensional shapes. They've been working with tiles and grid paper exploring how perimeter changes even though the area stays constant and how area changes as the perimeter remains constant. They've examined a set of parallelograms with the same base and height but very different slanted side lengths and discovered that they all have the same area.
The teacher decided to incorporate quilting into the lesson. The teacher used the internet to show the students samples of quilt patterns and they had a jubilant discussion about the patterns and the use of geometric shapes. The students were given one inch grid paper and told to draw a six inch square and then make a quilt design in the square. Part of the process will include finding the area and perimeter of the shapes that they will include in their pattern. The squares will then be put together to make a paper quilt for the class which will be displayed for the remainder of the unit.
The buzz in the classroom of students making their quilt square and figuring out how to draw a 3-D cube and a non-square parallelogram was infectious!
A seventh grade teacher has partnered with the First Wind Company to help provide suggestions for the relocation of an orphaned wind turbine, named Annie. Students will: calculate and measure distances, do some statistics, compare and scale, and apply several of the CCSS Mathematical Practices. The students are excited and will present their work and suggestions for a new location for Annie, to the First Wind Company.
These are two are examples of teachers ways in which I'm seeing teachers transform their curriculum to include application of concepts that the students are learning in math class.
Steve's words, "... capture engaging, concept-oriented, problem-solving, driven mathematics," (pg. 64) indicate what I'd like all students to experience on a regular basis in math class. This type of class has a lot to do with the teacher and his/her approach to the teaching and learning of mathematics. I think hard about how to help teachers bring this excitement for learning math into their classrooms.

Well I've been a bit late on this assignment, for a couple of reasons: I don't have a class to work with; and, I've been in Florida, at the beach and on the golf course, and 80 degree weather tends to make one more into those activities than a hard concentration on a math project. However, I'm back and have given considerable thought to a project I'd love to do with kids (if I only had a class). I enjoyed Leinwand's examples of real world math and communications, and they caused me to think about the essential matter of student engagement and group discussion around a common interest/set of problems to solve.
I raise bees as a hobby and every year teachers in different schools have asked if I would come and demonstrate to the kids how bees live, work and make honey. It's generally related to a science lesson(s) on insects; but I'm thinking that there is considerable mathematics which can involve student study, research, graphing, learning basic statistical measures like mean, median and mode, cost calculations,marketing and profit. If one wanted to integrate some science and/or social studies as well, there are topics such as pollination, disease, genetically modified seeds, charity organizations like the Heifer Project and their relationship to stemming world hunger, etc. So, my project will have several learning targets: Develop an understanding of the differences between mean, median and mode through activities of weights and measures, comparative shopping, and timing of honey crystallization; learn the process of spinning honey; use estimations to facilitate reasoning; calculate cost, profit and loss.
As an opener, I'd display a few bees (dead, of course) and a large container of honey and ask what's the relationship between them, and assuming they'll comment that bees make honey, I'd ask how anything that small can make so much to fill a hive box that weighs up to 100 pounds (and, they'll do that up to three times in a summer!) For some kids, you could ask what's the ratio between 3 lbs. of bees (the standard one purchases for one hive) and a 100 lbs. of honey. I would continue by having the class weigh an empty super (the name of a hive box where honey is stored), and then weigh a full one and ask them to calculate the difference. This gives them a sense of the volume of honey made in one super They'll also use this difference later to calculate the potential amount, in lbs. and ounces, they could pour in containers and sell in their school. And related to this will be an activity where the teacher asks them to shop with their parent (for observational purposes) and compare the prices of different sizes of honey jars, different producers' pricing and perhaps even the differences between stores and a local farmers market. All of these data are brought to school and teams of students will chart them for comparative purposes, as well as to calculate the mean, median and mode in pricing in the different venues, and for different sizes. They can have a discussion about how much they think they might charge if they sell their honey (because the next activity is to spin) in their school, and why they'd charge that amount. So on to spinning - first we'll have a couple students weigh the empty spinner - we'd set up the equipment to spin 10 frames, having weighed each one first (so they can again calculate the average weight per frame) and commence spinning the honey. The teacher can also ask for opinions (and have the kids chart them) as to how much total honey (in lbs.) they estimate they'll draw. When the draw is completed, they can again weigh the spinner and compare their earlier answers to the amount they estimated. The next step is to fill containers (we'll use 12 or 16 oz. containers); as they are doing that, have them calculate how many 12 or 16 oz. containers will be filled by that much honey if they use the old axiom, " a pint's a pound the world around". They can then calculate how much money will be gained if they sell every jar. After they have a figure, they can be asked, if we subtract the cost of the containers, how much will we have then? and lastly, they can have a problem question that speaks to the real value of total cost against total income, such as, if we calculate the cost of three pounds of bees, what will our profit be then? or, how much would we have to sell them for if we include the cost of the bees and the containers? This, of course, says nothing of their labor for spinning, filling jars and marketing. There are many additional components to this kind of endeavor with the kids; one is only limited by imagination and desire to take them to a real world set of experiences using their math.
Should any of my colleagues in this mathematical adventure we're all in, have an interest in constructing this unit with me, I'd be more than happy to collaborate and come to school to discuss it.

Also, Title IIB: Mathematics & Science Partnerships Projects have linked Middle Schools, High School math classes with Technical School faculty for hands-on projects. Meghan Southworth is the contact for the Title IIB Projects at the Maine Dept. of Ed.

STEM is also a great sources for math in context.

I have to connect here with the nod towards STEM! I have been very blessed to have been a part of a great opportuntiy to develop STEM curriculum for NASA along with 3 other teeachers. One is also from Maine. You can find our work herehttp://ares.jsc.nasa.gov/ares/eeab/ teachers.

I am so excited to read all the wonderful examples our teachers are using to apply mathematics in real life situations. Making the math CCSS come alive in applied situations is a real challenge. One really has to be attuned to how math is used all around us and take the time to go deeply into creating inquiry-based mathematical situations. We must be careful not to fall back to old habits of number problems without context on paper.

Michelle's NASA site is perfect for our STEM initiative at our middle school.

One of the examples I have used in the past with teaching students elapsed time is using the Cyr Bus Line schedule. They are asked to travel from Caribou to Bangor, etc. and figure out the times of a variety of bus trips. This is a real life example that students can apply. While I know my teaching and thinking need to pull in more examples of these to teach mathematical concepts, I struggle at times to come up with them. We live in an every day world and experience themselves but after long days of hard work I find it a struggle to generate them for my students. As the old saying goes, "Working hard but not smarter!" I plan to dive in, however, and do whatever I need to do in order to change my teaching style and watch the variety of lessons come to life in my classroom.

I feel I am a broken record in that I teach pre-service teachers, so I do not have classroom examples to show...but I loved the examples the author shared. I AM wondering whether having my pre-service students participate in such a task would impact them to transfer this to their future classroom. My interventions are on a much smaller scale, focused on problem-based learning, but not like these which are much lengthier case studies. Something to consider.

This chapter gave me hope and ideas to help some of our teachers develop lessons that will allow the children to experiment with math, talk math and, as the common core math standards require, work with math in real world situations.

I have done a unit with slope where the children research the ADA, measure our ramp at the school and make a decision if we are in compliance with the ADA. They write a letter to the school board explaining their findings and what they think can be done to improve access to our school. ...we have not received an answer or comment, yet.

I enjoyed reading the letters where the children were rewarded with a tangible product from the company but were also given another challenge that would spark further math. These offered higher level thinking and opportunities to see math out side of the classroom.

At one time it was "forward thinking" to bring in ads from the Sunday newspaper and have the children find percentages and total costs. Today it is so easy to access statistics, comparison of prices, etc on the internet that the children can easily create spread sheets, graphs and tables in effort to see, talk and experience mathematics. Technology is a math teachers best friend when doing a unit on data and statistics.